I'm wondering how many people it would take to start a new civilization. I'm thinking generally speaking in the following scenarios:

Scenario A) A group of people are exiled from their home. They are forced out into the wilderness [let's assume for the sake of argument that it's a pretty temperate and mild wilderness] and the population settles and thrives. They farm and reproduce (at an steady or exponential rate) how many people would you need to prevent crippling lack of genetic diversity? If there was an insufficient number, how many generations approximately would it be before crippling lack of genetic diversity set in?

Scenario B) In a post-apocalyptic scenario or future scenario wherein humans had to populate a planet either through colonization or through post-apocalyptic repopulation, how many humans would it take to repopulate?

Scenario C) If humans knew that they were facing an extinction crisis, what population control measures/laws could be feasibly adopted by governments to try and make sure that even though the initial genetic pool may be small. For example, would requiring every family to have a certain number of children and approving marriages to ensure that they allow for the greatest genetic diversity impact it at all?

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$\begingroup$Welcome to Worldbuilding.SE. There are many questions in one go. And this is coupled to different scenarii. I'd recommend to split it in different questions, to get more precise answers.$\endgroup$
– bilbo_pingouinJul 14 '15 at 9:37

So if you say that population settles and thrives, farms and reproduces, I would say that no more than the same amount of people that you could find in a small town are required. I'd say a small town because I considered that houses are to be built, earth is to be reaped and sowed, illnesses are to be cured and the population is to be defended (wilderness).

Scenario B) No matter what, I'd say that any effort would be a failure. As "post-apocalyptic" I imagine a world in which most of the advanced technology is no more at hand, where people have to continue killing and polluting in order to manage to survive, medical care is nonexistant, food is scarce, plants and wildlife are easily contaminated (virus, bacteria, radiations...)

Scenario C) Women and men should be forced to mate (in an extinction case, I would say that everyone would not feel forced anymore) and all the possibilities of cross-breeding should be tried, women should be specially protected (people going "we are all going to die, therefore I will shoot you with an AK47 now"). While a fertile man can mate multiple times in a short timespan, a woman requires at least 9 months to breed and the lack of time is a decisive factor to avoid an extiction. Fertile people should anyway treated with attention and care (medical most of all), while men and women that are not able to breed would be processed by their utility ("Can you find a cure for this disease? Ok, you are in. Can you produce more than you need? No, ok you are going to be converted into food").

The last scenario is the most interesting one from my point of view, since it can create a sort of "biotechnocracy/matriarchy" in the long time